H~4(BK, Z) and Operator Algebras

摘要

There is a well-known interpretation of group cohomology in terms of (generalized) group extensions. For a connected semisimple compact Lie group K, we prove that the extensions corresponding to classes in H~4(BK, Z) can be interpreted in terms of automorphisms of a pair consisting of a type II_1 von Neumann algebra and a Cartan subalgebra.